Typically, in Bayesian inverse problems in scientific computing, one is interested in inferring an unknown quantity \({\theta }\)  from some noisy observed data \({\mathbf {y}}= G({\theta }^*) + {e}\)  with \(G\)  denoting the parameter-to-observable map and \({e}\)  being the noise; see, e.g., [1]}, [2]}, [3]}. Let \(\pi _0\)  be the prior and consider zero-mean Gaussian noise with covariance \({\Gamma }\) , then the posterior is given by
\(\pi ( {\theta }) = \frac{1}{Z} \exp \left( -\frac{1}{2}\Vert  {\mathbf {y}}- G({\theta }) \Vert _{{\Gamma }^{-1}}^2 \right) \pi _0( {\theta })\, ,\) 
